Determination of formation anisotropy using multi-frequency processing of induction measurements with transverse induction coils

ABSTRACT

Skin-effect corrections are applied to measurements made by a transverse induction logging tool to give corrected measurements indicative of vertical conductivities of a formation. Data from a conventional induction logging tool are inverted or focused to give an isotropic model of formation resistivity. A forward modeling is used to derive from the isotropic model measurements that would be expected with a transverse induction logging tool. Skin-effect corrections are applied to these expected measurements. The formation anisotropy is determined from the skin-effect corrected transverse induction measurements, the skin-effect corrected expected measurements and from the isotropic model conductivities.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The invention is related generally to the field of interpretationof measurements made by well logging instruments for the purpose ofdetermining the properties of earth formations. More specifically, theinvention is related to a method for determination of anisotropicformation resistivity using multifrequency, multicomponent resistivitydata.

[0003] 2. Background of the Art

[0004] Electromagnetic induction and wave propagation logging tools arecommonly used for determination of electrical properties of formationssurrounding a borehole. These logging tools give measurements ofapparent resistivity (or conductivity) of the formation that whenproperly interpreted are diagnostic of the petrophysical properties ofthe formation and the fluids therein.

[0005] The physical principles of electromagnetic induction resistivitywell logging are described, for example, in, H. G. Doll, Introduction toInduction Logging and Application to Logging of Wells Drilled with OilBased Mud, Journal of Petroleum Technology, vol. 1, p.148, Society ofPetroleum Engineers, Richardson Tex. (1949). Many improvements andmodifications to electromagnetic induction resistivity instruments havebeen devised since publication of the Doll reference, supra. Examples ofsuch modifications and improvements can be found, for example, in U.S.Pat. No. 4,837,517; U.S. Pat. No. 5,157,605 issued to Chandler et al,and U.S. Pat. No. 5,452,761 issued to Beard et al.

[0006] A limitation to the electromagnetic induction resistivity welllogging instruments known in the art is that they typically includetransmitter coils and receiver coils wound so that the magnetic momentsof these coils are substantially parallel only to the axis of theinstrument. Eddy currents are induced in the earth formations from themagnetic field generated by the transmitter coil, and in the inductioninstruments known in the art these eddy currents tend to flow in groundloops which are substantially perpendicular to the axis of theinstrument. Voltages are then induced in the receiver coils related tothe magnitude of the eddy currents. Certain earth formations, however,consist of thin layers of electrically conductive materials interleavedwith thin layers of substantially non-conductive material. The responseof the typical electromagnetic induction resistivity well logginginstrument will be largely dependent on the conductivity of theconductive layers when the layers are substantially parallel to the flowpath of the eddy currents. The substantially non-conductive layers willcontribute only a small amount to the overall response of the instrumentand therefore their presence will typically be masked by the presence ofthe conductive layers. The non-conductive layers, however, are the oneswhich are typically hydrocarbon-bearing and are of the most interest tothe instrument user. Some earth formations which might be of commercialinterest therefore may be overlooked by interpreting a well log madeusing the electromagnetic induction resistivity well logging instrumentsknown in the art.

[0007] The effect of formation anisotropy on resistivity loggingmeasurements have long been recognized. Kunz and Moran studied theanisotropic effect on the response of a conventional logging device in aborehole perpendicular to the bedding plane of t thick anisotropic bed.Moran and Gianzero extended this work to accommodate an arbitraryorientation of the borehole to the bedding planes.

[0008] Rosthal (U.S. Pat. No. 5,329,448) discloses a method fordetermining the horizontal and vertical conductivities from apropagation or induction well logging device. The method assumes that θ,the angle between the borehole axis and the normal to the bedding plane,is known. Conductivity estimates are obtained by two methods. The firstmethod measures the attenuation of the amplitude of the received signalbetween two receivers and derives a first estimate of conductivity fromthis attenuation. The second method measures the phase differencebetween the received signals at two receivers and derives a secondestimate of conductivity from this phase shift. Two estimates are usedto give the starting estimate of a conductivity model and based on thismodel, an attenuation and a phase shift for the two receivers arecalculated. An iterative scheme is then used to update the initialconductivity model until a good match is obtained between the modeloutput and the actual measured attenuation and phase shift.

[0009] Hagiwara shows that the log response of an induction-type loggingtool can be described by an equation of the form $\begin{matrix}{V \propto {\frac{i}{L^{3}}\left( {{{- 2}{^{\quad k\quad L}\left( {1 - {i\quad k\quad L}} \right)}} + {i\quad k\quad {l\left( {^{\quad k\quad \beta} - ^{\quad k\quad L}} \right)}}} \right)}} & (1)\end{matrix}$

[0010] where

β²=cos² θ+sin² θ  (2)

[0011] and

k ²=ω²μ(ε_(h) +iσ _(h)/ω)   (3)

[0012] where L is the spacing between the transmitter and receiver, k isthe wavenumber of the electromagnetic wave, μ is the magneticpermeability of the medium, θ is the deviation of the borehole anglefrom the normal to the formation, λ is the anisotropy factor for theformation, ω is the angular frequency of the electromagnetic wave, σ_(h)is the horizontal conductivity of the medium and ε_(h) is the horizontaldielectric constant of the medium.

[0013] Eq. (3) is actually a pair of equations, one corresponding to thereal part and one corresponding to the imaginary part of the measuredsignal, and has two unknowns. By making two measurements of the measuredsignal, the parameters k and β can be determined. The two neededmeasurements can be obtained from (1) R and X signals from inductionlogs, (2) phase and attenuation measurements from induction tools, (3)phase or attenuation measurements from induction tools with twodifferent spacings, or (4) resistivity measurements at two differentfrequencies. In the low frequency limit, ε can be neglected in Eq. (3)and from known values of ω and μ, the conductivity σ can be determinedfrom k, assuming a value of μ equal to the permittivity of free space

[0014] Wu (U.S. Pat. No. 6,092,024) recognized that the solution to eqs.(1)-(3) may be nonunique and showed how this ambiguity in the solutionmay be resolved using a plurality of measurements obtained from multiplespacings and/or multiple frequencies.

[0015] One solution to the limitation of the induction instruments knownin the art is to include a transverse transmitter coil and a transversereceiver coil on the induction instrument, whereby the magnetic momentsof these transverse coils is substantially perpendicular to the axis ofthe instrument. Such as solution was suggested in Tabarovsky and Epov,“Geometric and Frequency Focusing in Exploration of Anisotropic Seams”,Nauka, USSR Academy of Science, Siberian Division, Novosibirsk, pp.67-129 (1972). Tabarovsky and Epov suggest various arrangements oftransverse transmitter coils and transverse receiver coils, and presentsimulations of the responses of these transverse coil systems configuredas shown therein. Tabarovsky and Epov also describe a method ofsubstantially reducing the effect on the voltage induced in transversereceiver coils which would be caused by eddy currents flowing in thewellbore and invaded zone. The wellbore is typically filled with aconductive fluid known as drilling mud. Eddy currents which flow in thedrilling mud can substantially affect the magnitude of voltages inducedin the transverse receiver coils. The wellbore signal reduction methoddescribed by Tabarovsky and Epov can be described as “frequencyfocusing”, whereby induction voltage measurements are made at more thanone frequency, and the signals induced in the transverse receiver coilsare combined in a manner so that the effects of eddy currents flowingwithin certain geometries, such as the wellbore and invasion zone, canbe substantially eliminated from the final result. Tabarovsky and Epov,however, do not suggest any configuration of signal processing circuitrywhich could perform the frequency focusing method suggested in theirpaper.

[0016] Strack et al. (U.S. Pat. No. 6,147,496) describe a multicomponentlogging tool comprising a pair of 3-component transmitters and a pair of3-component receivers. Using measurements made at two differentfrequencies, a combined signal is generated having a reduced dependencyon the electrical conductivity in the wellbore region. U.S. Pat. No. 5,781,436 to Forgang et al, the contents of which are fully incorporatedherein by reference, discloses a suitable hardware configuration formultifrequency, multicomponent induction logging.

[0017] U.S. Pat. No. 5,999,883 issued to Gupta et al, (the “Guptapatent”), the contents of which are fully incorporated here byreference, discloses a method for determination of an initial estimateof the horizontal and vertical conductivity of anisotropic earthformations. Electromagnetic induction signals induced by inductiontransmitters oriented along three mutually orthogonal axes are measuredat a single frequency. One of the mutually orthogonal axes issubstantially parallel to a logging instrument axis. The electromagneticinduction signals are measured using first receivers each having amagnetic moment parallel to one of the orthogonal axes and using secondreceivers each having a magnetic moment perpendicular to a one of theorthogonal axes which is also perpendicular to the instrument axis. Arelative angle of rotation of the perpendicular one of the orthogonalaxes is calculated from the receiver signals measured perpendicular tothe instrument axis. An intermediate measurement tensor is calculated byrotating magnitudes of the receiver signals through a negative of theangle of rotation. A relative angle of inclination of one of theorthogonal axes which is parallel to the axis of the instrument iscalculated, from the rotated magnitudes, with respect to a direction ofthe vertical conductivity. The rotated magnitudes are rotated through anegative of the angle of inclination. Horizontal conductivity iscalculated from the magnitudes of the receiver signals after the secondstep of rotation. An anisotropy parameter is calculated from thereceiver signal magnitudes after the second step of rotation. Verticalconductivity is calculated from the horizontal conductivity and theanisotropy parameter. One drawback in the teachings of Gupta et al isthat the step of determination of the relative angle of inclination ofthe required measurements of three components of data with substantiallyidentical transmitter-receiver spacings. Because of limitations on thephysical size of the tools, this condition is difficult to obtain;consequently the estimates of resistivities are susceptible to error. Inaddition, due to the highly nonlinear character of the response ofmulticomponent tools, such inversion methods are time consuming at asingle frequency and even more so at multiple frequencies.

[0018] Analysis of the prior art leads to the conclusion that knownmethods of determining anisotropic resistivities in real time requirevery low frequencies; as a consequence of the low frequencies, thesignal-to-noise ratio in prior art methods is quite low.

[0019] There is a need for a fast and robust method of determination ofanisotropic resistivity. Such a method should preferably be able to usehigh frequency measurements that are known to have bettersignal-to-noise ratio than low frequency methods. The present inventionsatisfies this need.

SUMMARY OF THE INVENTION

[0020] The present invention is a method of determination of horizontaland vertical conductivities of subsurface formations using a combinationof data acquired with a transverse induction logging tool such as the3DEX™ tool and data acquired with a conventional high definitioninduction logging tool (HDIL). 3DEX™ data are acquired at a plurality offrequencies and a multifrequency skin-effect correction is applied tothe 3DEX™ data. An isotropic resistivity model is derived from HDIL data(multiple frequency and multiple spacing). This may be done either byinversion or by focusing. Using a forward modeling program, expectedvalues of the transverse components of the 3DEX™ data for an isotropicmodel are derived. A skin-effect correction is applied to the modeloutput. Differences between the focused model output and the focusedacquired data are indicative of anisotropy and this difference is usedto derive an anisotropy factor.

[0021] In a preferred embodiment of the invention, a Taylor seriesexpansion is used to approximate the TILT data and use is made of thefact that the coefficient of the ω^(3/2) is relatively insensitive toborehole and invasion effects.

BRIEF DESCRIPTION OF THE FIGURES

[0022]FIG. 1 shows an induction instrument disposed in a wellborepenetrating earth formations.

[0023]FIG. 2 shows the arrangement of transmitter and receiver coils ina preferred embodiment of the present invention marketed under the name3DExplorer™

[0024]FIG. 3 shows the model used in the present invention.

[0025]FIG. 4 is a flow chart illustrating steps comprising the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

[0026] Referring now to FIG. 1, an electromagnetic induction welllogging instrument 10 is shown disposed in a wellbore 2 drilled throughearth formations. The earth formations are shown generally at 4. Theinstrument 10 can be lowered into and withdrawn from the wellbore 2 bymeans of an armored electrical cable 6 or similar conveyance known inthe art. The instrument 10 can be assembled from three subsections: anauxiliary electronics unit 14 disposed at one end of the instrument 10;a coil mandrel unit 8 attached to the auxiliary electronics unit 14; anda receiver/signal processing/telemetry electronics unit 12 attached tothe other end of the coil mandrel unit 8, this unit 12 typically beingattached to the cable 6.

[0027] The coil mandrel unit 8 includes induction transmitter andreceiver coils, as will be further explained, for inducingelectromagnetic fields in the earth formations 4 and for receivingvoltage signals induced by eddy currents flowing in the earth formations4 as a result of the electromagnetic fields induced therein.

[0028] The auxiliary electronics unit 14 can include a signal generatorand power amplifiers (not shown) to cause alternating currents ofselected frequencies to flow through transmitter coils in the coilmandrel unit 8.

[0029] The receiver/signal processing/telemetry electronics unit 12 caninclude receiver circuits (not shown) for detecting voltages induced inreceiver coils in the coil mandrel unit 8, and circuits for processingthese received voltages (not shown) into signals representative of theconductivities of various layers, shown as 4A through 4F of the earthformations 4. As a matter of convenience the receiver/signalprocessing/telemetry electronics unit 12 can include signal telemetry totransmit the conductivity-related signals to the earth's surface alongthe cable 6 for further processing, or alternatively can store theconductivity related signals in an appropriate recording device (notshown) for processing after the instrument 10 is withdrawn from thewellbore 2.

[0030] Turning now to FIG. 2, the configuration of transmitter andreceiver coils in a preferred embodiment of the 3DExplorer™ inductionlogging instrument of Baker Hughes is disclosed. Such a logginginstrument is an example of a transverse induction logging tool. Threeorthogonal transmitters 101, 103 and 105 that are referred to as theT_(x), T_(z), and T_(y) transmitters are shown (the z-axis is thelongitudinal axis of the tool). Corresponding to the transmitters 101,103 and 105 are associated receivers 107, 109 and 111, referred to asthe R_(x), R_(z), and R_(y) receivers, for measuring the correspondingmagnetic fields H_(xx), H_(zz), and H_(yy). In addition, the receivers113 and 115 measure two cross-components H_(xy), and H_(xz) of themagnetic field produced by the x- component transmitter.

[0031]FIG. 3 is a schematic illustration of the model used in thepresent invention. The subsurface of the earth is characterized by aplurality of layers 201 a, 201 b, . . . 201 i. The layers havethicknesses denoted by h₁, h₂, . . . h_(i). The horizontal and verticalresistivities in the layers are denoted by R_(h1), R_(h2), . . . R_(hi)and R_(v1), R_(v2), . . . R_(vi) respectively. Equivalently, the modelmay be defined in terms of conductivities (reciprocal of resistivity).The borehole is indicated by 202 and associated with each of the layersare invaded zones in the vicinity of the borehole wherein borehole fluidhas invaded the formation and altered is properties so that theelectrical properties are not the same as in the uninvaded portion ofthe formation. The invaded zones have lengths L_(x01), L_(x02), . . .L_(x0i) extending away from the borehole. The resistivities in theinvaded zones are altered to values R_(x01), R_(x02), . . . R_(x0i). Inthe embodiment of the invention discussed here, the invaded zones areassumed to be isotropic while an alternate embodiment of the inventionincludes invaded zones that are anisotropic, i.e., they have differenthorizontal and vertical resistivities. It should further be noted thatthe discussion of the invention herein may be made in terms ofresistivities or conductivities (the reciprocal of resistivity).

[0032] Turning now to FIG. 4, a flow chart of the method of the presentinvention is shown. Multifrequency, multicomponent induction data areobtained using, for example, the 3DEX™ tool, and a multifrequencyskin-effect correction is applied to these data 309. As disclosed inU.S. Pat. No. 5,703,773 to Tabarovsky et al., the contents of which arefully incorporated herein by reference, the response at multiplefrequencies may be approximated by a Taylor series expansion of theform: $\begin{matrix}{\begin{bmatrix}{\sigma_{a}\left( \omega_{1} \right)} \\{\sigma_{a}\left( \omega_{2} \right)} \\ \\{\sigma_{a}\left( \omega_{m - 1} \right)} \\{\sigma_{a}\left( \omega_{m} \right)}\end{bmatrix} = {\begin{bmatrix}1 & \omega_{1}^{1/2} & \omega_{1}^{3/2} & & \omega_{1}^{n/2} \\1 & \omega_{2}^{1/2} & \omega_{1}^{3/2} & & \omega_{2}^{n/1} \\ & & & & \\1 & \omega_{m - 1}^{1/2} & \omega_{m - 1}^{3/2} & & \omega_{m - 1}^{n/2} \\1 & \omega_{m}^{1/2} & \omega_{m}^{3/2} & & \omega_{m}^{n/2}\end{bmatrix}\begin{bmatrix}s_{0} \\s_{1/2} \\ \\s_{{({n - 1})}/2} \\s_{n/2}\end{bmatrix}}} & (4)\end{matrix}$

[0033] In a preferred embodiment of the invention, the number m offrequencies ω is ten. In eq.(4), n is the number of terms in the Taylorseries expansion. This can be any number less than or equal to m. Thecoefficient s_(3/2) of the ω^(3/2) term (ω being the square of k, thewave number) is generated by the primary field and is relativelyunaffected by any inhomogeneities in the medium surround the logginginstrument, i.e., it is responsive primarily to the formation parametersand not to the borehole and invasion zone. In a preferred embodiment ofthe invention, this is used as an estimate of the skin-effect correctedtransverse induction data. Specifically, these are applied to the H_(xx)and H_(yy) components. those versed in the art would recognize that in avertical borehole, the H_(xx) and H_(yy) would be the same, with bothbeing indicative of the vertical conductivity of the formation. In oneembodiment of the invention, the sum of the H_(xx) and H_(yy) is used soas to improve the signal to noise ratio (SNR).

[0034] Other methods of skin effect correction may also be used in thepresent invention. An example is that disclosed in U.S. Pat. No.5,666,057 to Beard et al., the contents of which are fully incorporatedherein by reference. Beard teaches the use of a polynomial curve fittingto the multifrequency data; constraints on the slope of the derivedpolynomial are used to obtain a skin-effect corrected signal.

[0035] Along with the 3DEX™, the present method also uses data from aprior art High Definition Induction Logging (HDIL) tool havingtransmitter and receiver coils aligned along the axis of the tool. Thesedata are inverted using a method such as that taught by Tabarovsky etal, or by U.S. Pat. No. 5,884,227 to Rabinovich et al., the contents ofwhich are fully incorporated herein by reference, to give an isotropicmodel of the subsurface formation 301. Instead of, or in addition to theinversion methods, a focusing method may also be used to derive theinitial model. Such focusing methods would be known to those versed inthe art and are not discussed further here. As discussed above, the HDILtool is responsive primarily to the horizontal conductivity of the earthformations when run in a borehole that is substantially orthogonal tothe bedding planes. The inversion method taught by Tabarovsky et al andby Rabinovich et al are computationally fast and may be implemented inreal time. This inversion give an isotropic model of the horizontalconductivities (or resistivities) in FIG. 3.

[0036] Using the isotropic model derived at 301, a forward modeling isused to calculate a synthetic response of the 3DEX™ tool 303 at aplurality of frequencies. A suitable forward modeling program for thepurpose is disclosed in Tabarovsky and Epov “Alternating ElectromagneticField in an Anisotropic Layered Medium” Geol. Geoph., No. 1. pp.101-109. (1977). Skin-effect corrections are then applied to thesesynthetic data 305. In a preferred embodiment of the invention, themethod taught by Tabarovsky is used for the purpose. Alternatively, andby way of example, the method taught by by Beard et al. may be used.

[0037] In the absence of anisotropy, the output from 305 should beidentical to the output from 309. Denoting by σ_(iso) the skin-effectcorrected transverse component synthetic data from 305 and by σ_(meas)the skin-effect corrected field data from 309, the anisotropy factor λis then calculated based on the following derivation:

[0038] The H_(xx) for an anisotropic medium is given by $\begin{matrix}{H_{xx} = {- {\frac{M}{4L^{3}}\left\lbrack {{- \left( \frac{L}{\delta_{v}} \right)^{2}} + {\left( {\frac{1}{3} + \frac{1}{\lambda}} \right)\left( \frac{L}{\delta_{h}} \right)^{3}}} \right\rbrack}}} & (5)\end{matrix}$

[0039] where${\delta_{v} = \sqrt{\frac{2}{\omega \quad \mu \quad \sigma_{v}}}},{\delta_{h} = \sqrt{\frac{2}{\omega \quad \mu \quad \sigma_{h}}}},{\lambda = {\frac{\sigma_{h}}{\sigma_{v}}.}}$

[0040] For a three-coil subarray, $\begin{matrix}{H_{xx} = {{- \frac{1}{4\pi}}\left( {\frac{1}{3} + \frac{1}{\lambda}} \right)\left( \frac{\omega \quad \mu \quad \sigma_{h}}{2} \right)^{3/2}{\sum M_{i}}}} & (6)\end{matrix}$

[0041] Upon introducing the apparent conductivity for H_(xx) this gives$\sigma_{meas}^{3/2} = {{\frac{3}{4}\left( {\frac{1}{3} + \frac{1}{\lambda}} \right)\sigma_{h}^{3/2}\quad {{or}\left( {\sigma_{meas}^{3/2} - \sigma_{iso}^{3/2}} \right)}} = {{\sigma_{h}^{3/2}\left( {\frac{1}{4} + \frac{3}{4\lambda} - 1} \right)} = {\sigma_{h}^{3/2}\left( {\frac{3}{4\lambda} - \frac{3}{4}} \right)}}}$

[0042] which gives the result $\begin{matrix}{\lambda = \frac{1}{1 - {\frac{4}{3}\left( \frac{\sigma_{iso}^{3/2} - \sigma_{meas}^{3/2}}{\sigma_{t}^{3/2}} \right)}}} & (7)\end{matrix}$

[0043] where σ_(t) is the conductivity obtained from the HDIL data,i.e., the horizontal conductivity. The vertical conductivity is obtainedby dividing σ_(t) by the anisotropy factor from eq. (5).

[0044] The present invention has been discussed above with respect tomeasurements made by a transverse induction logging tool conveyed on awireline. This is not intended to be a limitation and the method isequally applicable to measurements made using a comparable tool conveyedon a measurement-while-drilling (MWD) assembly or on coiled tubing.

[0045] While the foregoing disclosure is directed to the preferredembodiments of the invention, various modifications will be apparent tothose skilled in the art. It is intended that all variations within thescope and spirit of the appended claims be embraced by the foregoingdisclosure.

What is claimed is:
 1. A method of logging of subsurface formationsincluding at least one layer having a horizontal conductivity and avertical conductivity, the method comprising: (a) conveying anelectromagnetic logging tool into a borehole in the subsurfaceformations; (b) using said electromagnetic logging tool for obtaining,at each of a plurality of frequencies, at least one measurementindicative of at least one of said vertical conductivities; (c) applyinga skin-effect correction to said at least one measurement at saidplurality of frequencies and obtaining a skin-effect correctedconductivity measurement associated with said at least one layer; (d)obtaining a model including, for said at least one layer, a layerthickness and a horizontal conductivity; (e) determining an expectedvalue of said at least one skin-effect corrected conductivitymeasurement from said model; (f) determining from said skin effectcorrected measurement, said expected value of the skin-effect correctedmeasurement, and said horizontal conductivity, a vertical conductivityof the at least one layer.
 2. The method of claim 1 wherein saidplurality of frequencies is less than ten.
 3. The method of claim 1wherein said at least one measurement is selected from the groupconsisting of (i) a H_(xx) component, (ii) a H_(yy) component, and,(iii) a sum of a H_(xx) and a H_(yy) component.
 4. The method of claim 1wherein applying said skin-effect correction further comprises using aTaylor series expansion.
 5. The method of claim 4 wherein said Taylorseries expansion is in half-integer powers of frequency.
 6. The methodof claim 5 wherein said skin-effect corrected conductivity measurementsis related to the coefficient of the three-half power of frequency inthe Taylor series expansion.
 7. The method of claim 1 wherein obtainingsaid model further comprises making measurements of a H_(zz) componentat a plurality of frequencies and inverting said H_(zz) components. 8.The method of claim 1 wherein obtaining said model further comprises:(A) making measurements of a H_(zz) component at a plurality of spacingsof a transmitter and a receiver on an electromagnetic logging tool; and(B) at least one of: (i) inverting of said H_(zz) components, and, (iii)focusing of said H_(zz) components.
 9. The method of claim 1 whereindetermining said expected value of said at least one skin-effectcorrected conductivity further comprises: (i) setting a verticalconductivity equal to a horizontal conductivity; and (ii) using aforward modeling program to obtain at least one of: (A) an expectedH_(xx) component, and, (B) an expected H_(yy) component; wherein saidexpected components are obtained at a plurality of frequencies.
 10. Themethod of claim 9 wherein determining said expected value of said atleast one skin-effect corrected conductivity further comprises applyinga skin-effect correction to said expected components.
 11. The method ofclaim 10 wherein determining a vertical conductivity of the at least onelayer further comprises using a relationship of the form$\lambda = \frac{1}{1 - {\frac{4}{3}\left( \frac{\sigma_{iso}^{3/2} - \sigma_{meas}^{3/2}}{\sigma_{t}^{3/2}} \right)}}$

wherein λ is an anisotropy ratio, σ_(ISO) is said expected value of saidat least one skin-effect corrected conductivity measurement from saidmodel, σ_(meas) is said skin-effect corrected conductivity measurement,and σ_(t) is said horizontal conductivity.
 12. A method of determining aparameter of interest of subsurface formations including a plurality oflayers each having a horizontal resistivity and a vertical resistivity,the method comprising: (a) using sensors on an electromagnetic loggingtool conveyed in a borehole in the subsurface formations and makingmeasurements indicative of said horizontal conductivities; (b) derivingfrom said measurements indicative of horizontal conductivities anisotropic model of said subsurface formations, (c) using sensors on anelectromagnetic logging tool conveyed in a borehole in the subsurfaceformations and making measurements indicative of said verticalconductivities; (d) applying a skin-effect correction to saidmeasurements in (c) at said plurality of frequencies and obtaining askin-effect corrected conductivity measurement; (d) using a modelingprogram and determining from said isotropic model expected measurementscorresponding to said skin-effect corrected conductivity measurementsand applying skin-effect corrections to said expected measurements; (f)determining from said skin-effect corrected measurements, correspondingskin-effect corrected expected measurements, and said isotropic model,said parameter of interest.
 13. The method of claim 12 wherein saidparameter of interest is a vertical conductivity of one of saidplurality of layers.
 14. The method of claim 12 wherein using saidsensors further comprises making measurements at a plurality offrequencies.
 15. The method of claim 14 wherein said plurality offrequencies is less than eight.
 16. The method of claim 12 wherein saidmeasurements indicative of vertical conductivities comprise at least oneof: (i) a H_(xx) component, (ii) a H_(yy) component, and, (iii) a sum ofthe H_(xx) and H_(yy) components.
 17. The method of claim 12 whereinapplying said skin-effect correction further comprises using a Taylorseries expansion of said at least one component.
 18. The method of claim17 wherein said Taylor series expansion is in half-integer powers offrequency.
 19. The method of claim 18 wherein said skin-effect correctedconductivity measurements is related to the coefficient of thethree-half power of frequency in the Taylor series expansion.
 20. Themethod of claim 12 wherein deriving said isotropic model furthercomprises at least one of: (i) inversion of a H_(zz) component at aplurality of frequencies, (ii) inversion of a H_(zz) component acquiredwith a plurality of spacings of a transmitter and a receiver on thelogging tool of (a), and, (iii) focusing of a H_(zz) acquired with aplurality of spacings of a transmitter and receiver on the logging toolof (a).
 21. The method of claim 12 further comprising determining saidexpected measurements at a plurality of frequencies, and whereinapplying skin effect corrections to said expected measurements furthercomprises using a Taylor series expansion in half integer powers offrequency.
 22. The method of claim 12 wherein determining the parameterof interest further comprises using a relationship of the form$\lambda = \frac{1}{1 - {\frac{4}{3}\left( \frac{\sigma_{iso}^{3/2} - \sigma_{meas}^{3/2}}{\sigma_{t}^{3/2}} \right)}}$

wherein λ is an anisotropy ratio, σ_(iso) is said expected value of saidat least one skin-effect corrected conductivity measurement from saidmodel, σ_(meas) is said skin-effect corrected conductivity measurement,and σ_(t) is a resistivity in said isotropic model.